Question

В сосуд , содержащий 8 литров 24 процентного водного раствора некоторого вещества, добавили 4 литра воды. Сколько процентов составляет концентрация получившегося раствора? Смешали 3 литра 35 процентного водного раствора некоторого вещества с 12 литрами 15 процентного водного раствора этого же вещества .Сколько процентов составляет концентрация получившегося раствора? Смешали 9 литров 40 процентного водного раствора некоторого вещества с 11 литрами 20 процентного водного раствора этого же вещества . Сколько процентов составляет концентрация получившегося раствора?

Answer 1

1) 8×(1-0.24)=6.08л - кол-во воды в растворе
8-6.08=1.92л - кол-во вещества
8+4=12л - всего нового раствора
составим пропорцию:
12 - 100%
1.92 - х%
$x = \frac{1.92 \times 100}{12} \\ x = 16\%$
2)3×0.35=1.05л - вещества в первом растворе
12×0.15=1.8л - вещества во втором растворе
3+12=15л - объем нового раствора
1.05+1.8=2.85л - вещества в новом растворе

составим пропорцию:
15-100%
2.85-х
$x = \frac{2.85 \times 100}{15} \\ x = 19\%$
3)9×0.4+11×0.2=5.8л - вещества в новом растворе
9+11=20л - объем нового вещества

составим пропорцию:
20-100%
5.8-х
$x = \frac{5.8 \times 100}{20} \\ x = 29\%$

Answer 2

Calculation of Concentration of the Solution

To calculate the concentration of the resulting solution, we need to consider the initial concentration of the solution and the amount of water added. Let's calculate the concentration for each scenario:

1. In the first scenario, we have a vessel containing 8 liters of a 24% aqueous solution of a substance. We add 4 liters of water to this solution. We need to calculate the concentration of the resulting solution.

- Initial volume of the solution: 8 liters - Initial concentration of the solution: 24% - Amount of water added: 4 liters

To calculate the concentration of the resulting solution, we can use the formula:

Concentration = (Initial volume of the solution * Initial concentration of the solution) / (Final volume of the solution)

Substituting the values into the formula:

Concentration = (8 liters * 24%) / (8 liters + 4 liters)

Simplifying the expression:

Concentration = 192% / 12 liters

Therefore, the concentration of the resulting solution is 16%.

2. In the second scenario, we mix 3 liters of a 35% aqueous solution of a substance with 12 liters of a 15% aqueous solution of the same substance. We need to calculate the concentration of the resulting solution.

- Volume of the first solution: 3 liters - Concentration of the first solution: 35% - Volume of the second solution: 12 liters - Concentration of the second solution: 15%

To calculate the concentration of the resulting solution, we can use the formula:

Concentration = (Volume of the first solution * Concentration of the first solution + Volume of the second solution * Concentration of the second solution) / (Total volume of the resulting solution)

Substituting the values into the formula:

Concentration = (3 liters * 35% + 12 liters * 15%) / (3 liters + 12 liters)

Simplifying the expression:

Concentration = (105% + 180%) / 15 liters

Therefore, the concentration of the resulting solution is 17%.

3. In the third scenario, we mix 9 liters of a 40% aqueous solution of a substance with 11 liters of a 20% aqueous solution of the same substance. We need to calculate the concentration of the resulting solution.

- Volume of the first solution: 9 liters - Concentration of the first solution: 40% - Volume of the second solution: 11 liters - Concentration of the second solution: 20%

Using the same formula as before:

Concentration = (Volume of the first solution * Concentration of the first solution + Volume of the second solution * Concentration of the second solution) / (Total volume of the resulting solution)

Substituting the values into the formula:

Concentration = (9 liters * 40% + 11 liters * 20%) / (9 liters + 11 liters)

Simplifying the expression:

Concentration = (360% + 220%) / 20 liters

Therefore, the concentration of the resulting solution is 29%.

In summary, the concentrations of the resulting solutions are as follows: 1. The concentration of the resulting solution in the first scenario is 16%. 2. The concentration of the resulting solution in the second scenario is 17%. 3. The concentration of the resulting solution in the third scenario is 29%.